85 lines
2.5 KiB
C
85 lines
2.5 KiB
C
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/*
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* Double-precision SVE cos(x) function.
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*
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* Copyright (c) 2019-2023, Arm Limited.
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* SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception
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*/
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#include "sv_math.h"
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#include "pl_sig.h"
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#include "pl_test.h"
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#if SV_SUPPORTED
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#define InvPio2 (sv_f64 (0x1.45f306dc9c882p-1))
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#define NegPio2_1 (sv_f64 (-0x1.921fb50000000p+0))
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#define NegPio2_2 (sv_f64 (-0x1.110b460000000p-26))
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#define NegPio2_3 (sv_f64 (-0x1.1a62633145c07p-54))
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/* Original shift used in Neon cos,
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plus a contribution to set the bit #0 of q
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as expected by trigonometric instructions. */
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#define Shift (sv_f64 (0x1.8000000000001p52))
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#define RangeVal (sv_f64 (0x1p23))
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#define AbsMask (0x7fffffffffffffff)
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static NOINLINE sv_f64_t
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__sv_cos_specialcase (sv_f64_t x, sv_f64_t y, svbool_t cmp)
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{
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return sv_call_f64 (cos, x, y, cmp);
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}
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/* A fast SVE implementation of cos based on trigonometric
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instructions (FTMAD, FTSSEL, FTSMUL).
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Maximum measured error: 2.108 ULPs.
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__sv_cos(0x1.9b0ba158c98f3p+7) got -0x1.fddd4c65c7f07p-3
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want -0x1.fddd4c65c7f05p-3. */
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sv_f64_t
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__sv_cos_x (sv_f64_t x, const svbool_t pg)
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{
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sv_f64_t n, r, r2, y;
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svbool_t cmp;
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r = sv_as_f64_u64 (svand_n_u64_x (pg, sv_as_u64_f64 (x), AbsMask));
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cmp = svcmpge_u64 (pg, sv_as_u64_f64 (r), sv_as_u64_f64 (RangeVal));
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/* n = rint(|x|/(pi/2)). */
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sv_f64_t q = sv_fma_f64_x (pg, InvPio2, r, Shift);
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n = svsub_f64_x (pg, q, Shift);
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/* r = |x| - n*(pi/2) (range reduction into -pi/4 .. pi/4). */
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r = sv_fma_f64_x (pg, NegPio2_1, n, r);
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r = sv_fma_f64_x (pg, NegPio2_2, n, r);
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r = sv_fma_f64_x (pg, NegPio2_3, n, r);
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/* cos(r) poly approx. */
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r2 = svtsmul_f64 (r, sv_as_u64_f64 (q));
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y = sv_f64 (0.0);
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y = svtmad_f64 (y, r2, 7);
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y = svtmad_f64 (y, r2, 6);
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y = svtmad_f64 (y, r2, 5);
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y = svtmad_f64 (y, r2, 4);
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y = svtmad_f64 (y, r2, 3);
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y = svtmad_f64 (y, r2, 2);
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y = svtmad_f64 (y, r2, 1);
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y = svtmad_f64 (y, r2, 0);
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/* Final multiplicative factor: 1.0 or x depending on bit #0 of q. */
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sv_f64_t f = svtssel_f64 (r, sv_as_u64_f64 (q));
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/* Apply factor. */
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y = svmul_f64_x (pg, f, y);
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/* No need to pass pg to specialcase here since cmp is a strict subset,
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guaranteed by the cmpge above. */
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if (unlikely (svptest_any (pg, cmp)))
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return __sv_cos_specialcase (x, y, cmp);
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return y;
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}
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PL_ALIAS (__sv_cos_x, _ZGVsMxv_cos)
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PL_SIG (SV, D, 1, cos, -3.1, 3.1)
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PL_TEST_ULP (__sv_cos, 1.61)
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PL_TEST_INTERVAL (__sv_cos, 0, 0xffff0000, 10000)
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PL_TEST_INTERVAL (__sv_cos, 0x1p-4, 0x1p4, 500000)
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#endif
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